I heard that a wavefunction applies to a quantum system.

But what is a quantum system? I am new to quantum mechanics, sorry for asking a basic question.


The shortest answer is that a quantum system is any system that obeys the laws of quantum mechanics. This means that:

  1. The system's state at a given time is described by a vector in a complex vector space. This vector is called the system's wave function.
  2. The system's wave function evolves over time following the Schrodinger wave equation.
  3. Each attribute of the system that can be measured (an "observable") is represented by a linear operator on its vector space.
  4. The act of measuring an observable of the system causes the system's wave function to "collapse" to an eigenstate of the corresponding operator. The result of the measurement will be the eigenvalue of that eigenstate.
  5. The probability that a measurement of an observable of the system at a given time will return a given value is the squared modulus of the complex amplitude of the projection of its wave function (immediately before the measurement) onto the corresponding eigenstate.

This explanation probably gives rise to even more questions - "what is a complex vector space ?", "what is a linear operator ?", "what is an eigenstate ?" etc. - which are best answered by reading an introduction to quantum mechanics such as this one at Wikipedia

  • $\begingroup$ This is the shortest summary of QM I ever read. $\endgroup$ – Exocytosis Sep 30 '19 at 12:32
  • $\begingroup$ @Exocytosis These are basically the postulates of QM :) $\endgroup$ – Aaron Stevens Sep 30 '19 at 15:15

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